Answer:
The sign board must be placed 573 ft ahead of the exit.
Explanation:
Distance needed for reducing the speed from 55 mph to 25 mph is given as
[tex]d=\frac{v_f^2-v_i^2}{30 \times (\frac{a}{g}-G)}[/tex]
Here
[tex]d=\frac{v_f^2-v_i^2}{2 \times (\frac{a}{g}-G)}\\d=\frac{25^2-55^2}{30 \times (\frac{-5}{32.2}-0.01)}\\d=551 ft[/tex]
Now the perception time is 2.5 second, 20/20 vision person can read 6 inch letters from 60 x 6 ft.
For 20/40 vision person can read 6 inch letters from 30 x 6 ft=180 ft.
SSD is [tex]d=\frac{55 \times 5280 \times 2.5}{60 \times 60}\\d=202 ft[/tex]
So the minimum distance is given as
[tex]Minimum distance=551+202-180 ft\\Minimum distance=573 ft\\[/tex]
So the sign board must be placed 573 ft ahead of the exit.